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How to prove √X is irrational number

by SOHAWONG
Tags: √x, irrational, number, prove
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SOHAWONG
#1
Mar5-10, 08:13 PM
P: 16
when X is even number,it's easy to prove
but how about the condition which X is odd number?
I have no idea of this
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Hurkyl
#2
Mar5-10, 08:14 PM
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[itex]\sqrt{4}[/itex] is irrational?
SOHAWONG
#3
Mar5-10, 09:57 PM
P: 16
Quote Quote by Hurkyl View Post
[itex]\sqrt{4}[/itex] is irrational?
no,i may add despite 1,4,9,16,25...etc

Char. Limit
#4
Mar5-10, 11:25 PM
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How to prove √X is irrational number

So in other words...

[tex]\sqrt{x}[/tex] is irrational iff x=/=n^2 for n belonging to the integer set.
SOHAWONG
#5
Mar5-10, 11:54 PM
P: 16
Quote Quote by Char. Limit View Post
So in other words...

[tex]\sqrt{x}[/tex] is irrational iff x=/=n^2 for n belonging to the integer set.
yes, but how to prove?
Tinyboss
#6
Mar6-10, 12:49 AM
P: 234
Fundamental theorem of arithmetic. Assume p^2/q^2=x with gcd(p,q)=1, and see what has to divide what.
SOHAWONG
#7
Mar6-10, 06:33 PM
P: 16
Quote Quote by Tinyboss View Post
Fundamental theorem of arithmetic. Assume p^2/q^2=x with gcd(p,q)=1, and see what has to divide what.
what does gcd mean?
Tinyboss
#8
Mar6-10, 06:40 PM
P: 234
Greatest common divisor. If gcd(p,q)=1, it means the fraction p/q is in lowest terms.

Look at the proof for sqrt(2), and adapt it. Remember that "even" just means "is divisible by 2", so that if you're checking a number other than 2, you won't be thinking about "even" anymore.
skeptic2
#9
Mar6-10, 06:50 PM
P: 1,803
Although right now you're probably more interested in just getting the right answer, you might want to check out the following Wikipedia entries:
http://en.wikipedia.org/wiki/Square_root
http://en.wikipedia.org/wiki/Square_root_of_2

And for an interesting history of the discovery of irrational numbers look at
http://en.wikipedia.org/wiki/Irrational_number


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